1. Field of the Invention
The present invention relates to a method and program both for simulating the intensity distribution of an optical image, and particularly relates to a simulation method and program used for calculating the intensity distribution of an optical image to estimate the shape of a resist pattern to be formed in a lithography step of semiconductor device manufacturing. In addition, the present invention relates to a method of manufacturing semiconductor device using a pattern data generating method using this simulation method.
2. Description of the Related Art
When semiconductor devices are manufactured, a simulation technique is used to calculate the intensity distribution of an optical image to be formed in a resist film or the like on a substrate by photolithography. A lithography simulation calculates the intensity distribution of the optical image on the basis of optical conditions (for example, the wavelength of exposure light, the numerical aperture of a lens in a projection optical system, and an illumination shape) in the exposure system and information (for example, the indices of refraction and the thicknesses of films) on multiple films on the substrate. Moreover, the lithography simulation calculates the resist pattern in consideration of processes such as photoreaction, PEB (Post-exposure Bake) and development.
For the purpose of enabling the simulation to accurately calculate the intensity distribution of the optical image to be formed in the resist film, it is necessary to find a diffusant concentration distribution formed by a diffusant such as an acid diffusing in the resist film. A diffusion equation needs to be solved in order to find the concentration distribution. The diffusion equation is generally solved based on a solution using a difference method in which an arbitrary boundary condition can be used. If, however, the concentration distribution is intended to be found with high accuracy by use of the difference method, an associated problem is that the difference method consumes a larger amount of time for its calculation.
On the other hand, a proposal has been made on a method of fast and accurately solving the diffusion equation by use of a fast Fourier transform (see SPIE 2512-384, “A fast resist image estimation methodology using light intensity distribution,” for example). However, the fast Fourier transform needs to be applied to a system that satisfies a periodic boundary condition. For this reason, in a case where the intensity distribution of an optical image satisfies no periodic boundary condition, the fast Fourier transform can not be applied to simulate the intensity distribution.
Furthermore, another proposal has been made on a technique of expanding a resist film area where an optical image is to be formed for the purpose of satisfying the periodic boundary condition (see SPIE 3051-522, “A practical 3D lithography simulation system,” for example). A problem associated with this technique is that the application of the fast Fourier transform to the lithography simulation causes aliasing at the boundary part between the expanded resist film area and the original resist film area, and thus modulates the entire distribution. For this reason, the technique entails a problem that the application of the fast Fourier transform to such a lithography simulation is apt to decrease the accuracy.